Three-dimensional (3D) optical imaging of cells has been dominated by fluorescence confocal microscopy, wherein the specimen is typically fixed and tagged with exogenous fluorophores, as described, for example, in Pawley, Handbook of biological confocal microscopy (2006). The image, in confocal microscopy, is rendered serially, i.e., at successive depths, and the out-of-focus light is rejected by a pinhole in front of the detector.
Alternatively, 3D structure can also be obtained via deconvolution microscopy, in which a series of fluorescence images along the optical axis of the system is recorded, instead, as described in McNally et al., Three-dimensional imaging by deconvolution microscopy, Methods, vol. 19, pp. 373-85 (1999). The deconvolution numerically reassigns the out-of-focus light, instead of removing it, thus making better use of the available signal at the expense of increased computation time.
Of various biological imaging modalities, label-free methods are often preferable, especially when photobleaching and phototoxicity play a limiting role. Far-zone measurement of the scattering of electromagnetic fields, or of massive particles, has long been known to provide three-dimensional information with respect to the at the structure of weakly scattering media, and, in biology, for example, has enabled discoveries, from the structure of the DNA molecule to that of the ribosome. Despite the great success of methods based on scattering and analysis, such methods have suffered from the so-called “phase problem,” as discussed by Wolf, History and Solution of the Phase Problem in Theory of Structure Determination of Crystals from X-Ray Diffraction Measurements, in Advances in Imaging and Electron Physics (Hawkes, ed.) (2011), which is incorporated herein by reference. Reconstructing a 3D structure from measurements of scattered fields entails solving an inverse scattering problem, which, in turn, requires measurement of both the amplitude and phase of the scattered fields. The scattered fields are uniquely related to the structure of the object, however, measurement of the intensity alone does not suffice, because a given intensity may be produced by many combinations of fields, each corresponding to a different sample structure. The nonuniqueness inherent in intensity measurements may be overcome, under certain circumstances, by prior assumptions and within certain approximations.
In the optical regime, interferometric experiments may practicably yield not only the scattered intensity but the full complex scattered field, with holography serving as an example. Holographic data obtained from many view angles are sufficient for the unambiguous reconstruction of the sample. Such solution of the inverse scattering problem with light was presented by Wolf, and the approach became known as diffraction tomography. Various approaches for 3D reconstructions of transparent objects have been reported, such as Hillmann et al., Holoscopy—holographic optical coherence tomography, Opt. Lett., vol. 36, pp. 2390-92 (2011). Some of the drawbacks of diffraction tomography and of holographic optical coherence tomography (OCT) that render them inappropriate for bioimaging applications involving single cells. Neither OCT nor holographic techniques yield the necessary resolution for reconstructing the internal structure of a single cell. Holographic methods based on laser illumination suffer from speckles that degrade the contrast to noise ratio and ultimately the resolution of the image. On the other hand, OCT-based approaches are typically targeted toward deep tissue imaging rather than single cell imaging because the longitudinal resolution is typically larger than a cell thickness. Further, for backscattering methods such as OCT, the physical significance of the measured phase, crucial for the 3D reconstruction, is elusive because the spatial coherence of the field is degraded.
Further, QPI-based projection tomography has been applied to live cells, as described in Choi, et al., Tomographic phase microscopy, Nat. Methods, vol. 4, pp. 717-19 (2007). However, the approximation used in this computed tomography fails for high numerical aperture imaging, where diffraction and scattering effects are essential and drastically limit the depth of field that can be reconstructed reliably in live cells. This problem was recognized by Choi et al., who attempted to alleviate the problem by extending the depth of focus numerically, in Choi et al., Extended depth of focus in tomographic phase microscopy using a propagation algorithm, Opt. Lett., vol. 33, pp. 171-73 (2008). One of the disadvantages of the technique suggested by Choi et al. is that the propagation algorithm must be recursively applied at each depth d for which a solution is sought. Furthermore, the signal-to-noise degrades quickly outside the depth of field of the imaging optics, which hampers numerical reconstruction.
Haldar et al., Label-Free High-Resolution Imaging of Live Cells with Deconvolved Spatial Light Interference Microscopy, IEEE EMBC 2010, pp. 3382-85 (2010) teaches a deconvolution-based approach to spatial light interference microscopy based on determining, and then deconvolving, the point spread function (PSF) of the microscope in order to obtain two-dimensional imaging data.
Digital holography is another prior art method that has been applied to three-dimensional imaging, as described by Depeursinge, Digital holography applied to microscopy, in Digital Holography and Three-Dimensional Display (Poon, ed.), p. 98 (2006), incorporated herein by reference.
Spatial Light Interference Microscopy has been taught as a method of quantitative phase imaging (QPI) in U.S. patent application Ser. No. 12/454,660 (hereinafter, the Popescu '660 application), filed May 21, 2009, and incorporated herein by reference, and in references cited therein. The approximations employed therein, however, fail for high-numerical-aperture imaging, where diffraction and scattering effects are essential, and drastically limit the depth of field that can be reconstructed reliably.
QPI is an active field of study and among various experimental approaches that have been proposed and demonstrated are the techniques taught by Popescu, et al., Quantitative phase imaging of nanoscale cell structure and dynamics, in Methods in Cell Biology, vol. 90, pp. 87-115 (2008), incorporated herein by reference. Radon-transform-based reconstruction algorithms together with phase-sensitive measurements have enabled optical tomography of transparent structures, and, more recently, QPI-based projection tomography has been applied to live cells, as described, for example, by Choi et al., Tomographic phase microscopy, Nat. Methods, vol. 4, pp. 717-19 (2007). However, the approximation used in computed tomography, as described in any of the prior art listed above, fails for high-numerical-aperture imaging, where diffraction effects are significant and limit the depth of field that can be reconstructed reliably.